What is the limit as h approaches 0 of (4/(9+h)-4/9)/h ?

The limit as h approaches 0 of (4/(9+h)-4/9)/h is -4/81

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limit as h approaches 0 of (4/(9+h)-4/9)/h

h \to 0 lim (\frac{\frac{4}{9 + h} - \frac{4}{9}}{h})

- \frac{4}{81}

Decimal Notation

- 0.04938 \dots

Solution steps

h \to 0 lim (\frac{\frac{4}{9 + h} - \frac{4}{9}}{h})

Simplify

\frac{\frac{4}{9 + h} - \frac{4}{9}}{h} : - \frac{4}{9 ( h + 9 )}

= h \to 0 lim (- \frac{4}{9 ( h + 9 )})

Plug in the value

h = 0

= - \frac{4}{9 ( 0 + 9 )}

Simplify

= - \frac{4}{81}

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What is the limit as h approaches 0 of (4/(9+h)-4/9)/h ?
The limit as h approaches 0 of (4/(9+h)-4/9)/h is -4/81